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Interlude — the tap on the Titanic. Captain, what shall we do?. A bit after 11:30 on the night of Sunday April 14, 1912, you hear a terrible scraping noise on the hull beneath your cabin on the Titanic. Then you see a problem and run to tell the Captain about the trouble you have seen.
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Captain, what shall we do? A bit after 11:30 on the night of Sunday April 14, 1912, you hear a terrible scraping noise on the hull beneath your cabin on the Titanic. Then you see a problem and run to tell the Captain about the trouble you have seen.
When you tell the Captain that the tap in your bathroom has a faulty washer and is making a slight but definitely noticeable and constant drip, he seems very brave. He knows this leak can sink the great ship if given enough time, but he does not seem concerned. Brave indeed. Oh dear!
How long do we have Sir? You see the writing on the wall. This leaky tap will surely do us in. You desperately ask the Captain how long ‘til the end. The Captain refuses to even consider the possibility. Yes, he is brave through and through. Desperate for help, we find Mr. Thomas Andrews sitting quietly at a table sipping a stiff drink. Mr. Andrews designed the Titanic, and knows her through and through. We ask Mr. Andrews how long until the tap in the bathroom sinks us. Seeming oddly amused he sets out to help us.
Mr. Andrews says we must first approximate how much water is coming from the tap. I describe the situation to him poring a bit of water very slowly from a water glass. With is stopwatch he estimates that we will fill a tablespoon in about 15 seconds. Talk with Thomas Andrews
A tablespoon is 15 ml, so the tap is dripping at the rate of 15ml in 15 seconds. This is equivalent to a rate of 1 ml per second, or 60 ml per minute. Mr. Andrews decides to work with the rate of 60 ml per minute. Mr. Andrews at work
Mr. Andrews then explains to me that 1 ml of water has a mass of 1 gram. How wonderfully convenient this metric system is! So our tap is running at the rate of 60 grams of water per minute. Mr. Andrews at work
Mr. Andrews then informs me that there is also another leak in the ship. He says he has done a few calculations about this other leak as well. It seems this other leak is a bit bigger. In fact, it is contributing water at a rate of about 400 tonnes per minute. Shocking news!
He says that a tonne is a thousand kilograms (kg). So 400 tonnes is equal to 400,000 kilograms. As a kiliogram is 1000 grams, our 400 tonnes is equal to 400,000,000 grams. Mr. Andrews explains
Mr. Andrews explains As our tap is dripping 60 g per minute, and the leak below is contributing some 400,000,000 g per minute So the leak below is about 10 million times worse than the tap in my bathroom!
Mr. Andrews says that he calculated the leak below will take about 3 hours to sink the ship. He then calculated that as our leak is about one seven millionth as bad, that it will take some 2000 years for the tap in my bathroom to sink the ship. (Try it!) Oh dear!
Of course it is not good to leave a tap dripping, but my problem was really vastly smaller than another. It was nice of Mr. Andrews to spend his last hours explaining things to me. He even seemed to enjoy teaching me something. Boy, do I feel foolish
Is there any real point to this? Here we have exaggerated to a silly extent, but yes there is a point. In a situation where you are not familiar with things, a very basic amount of arithmetic can help you understand matters and make correct decisions. Often, the situations where you are not familiar with things will involve things taken past the point of our experience. In quantifying these things, even approximately, we will often wind up with big numbers. Arithmetic helps us understand numbers, big and small.
